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Agronomic irrigation design and scheduling
Shmulik FriedmanDepartment of Environmental Physics and Irrigation, Institute of Soil, Water and Environmental
Sciences (ARO), The Volcani Center, Rishon LeZion 7505101, Israel, [email protected]
Workshop on “The future of water for irrigation in California and Israel”Davis CA, July 16th, 2018
http:/app.agri.gov.il/didas
General design of drip irrigation
Dripper configurationDripper depths
Irrigation scheduling
Daily irrigation dose
Dripper discharge rate
profit = income – total costs
Daily irrigation dose
Yield
income
system costenergy cost
water costenergy cost
total costs
waterother factors
plantsoil
climate
plantsoil
climate
plant climate salinity
system costenergy costadditional costs
plantsoil
control
Brief introduction to agronomic irrigation design and scheduling Main principles of the DIDAS approachCoupled source-sink model for water uptake evaluation
Steady-state water flow and uptake module (for system design):Single emitter-root zone pairArrays of emitters and root zonesSubsurface drip irrigation(Yield – Plant Population Density relationship in sprinkler irrigation)
(Quasi steady-state water flow and uptake module)
Unsteady water flow and uptake module (for irrigation scheduling)Morning and all-day-long daily irrigationsEvery-few-days irrigations
Soil salinity module (for salinity management)
The DIDAS program – will be demonstrated briefly in the poster session
In this lecture:
Design and Scheduling of Drip Irrigation Systems•Distance between emitters along a drip line •Distance between drip lines•Depth of subsurface emitters•Emitter discharge rate•Irrigation frequency•Starting hour•Duration of irrigation •Daily irrigation dose
Drip (Trickle) Irrigation
on-surface sub-surface
annual crops
trees high pressure
low pressure
DIDAS- A New Approach and User-Friendly Software Package for
Assisting Drip Irrigation Design And Scheduling
Gregory Communar, Alon Gamliel and Shmulik FriedmanDepartment of Environmental Physics and Irrigation, Institute of Soil, Water and Environmental
Sciences (ARO), The Volcani Center, Rishon LeZion 7505101, Israel
http://app.agri.gov.il/didas
Previous suggestions based on analytical solutions to the water flow problem
Bresler (1978) recommended on using Wooding's (1968) solution for steady infiltration from a circular disk, describing the ponding zone around the emitter, and to determine the combination of emitter discharge and distance between emitters along the dripline according to a criterion of a threshold value
for the capillary pressure at mid-distance between emitters in the soil surface. Limitations of the approach: ignores water uptake; refers to an irrelevant location.
According to another, more realistic approach of Amoozegar-Fard et al. (1984)one should solve the problem of steady water flow from a source assuming a prescribed, constant and a priori known water uptake rate within a rooting zone of simple geometry (e.g. vertical cylinder or 1-D variation with depth), the design criterion being again threshold value for the capillary pressure at any depth within the active root zone midway between emitters. Limitations of the approach: water uptake is assumed to be knownrefers to an irrelevant location.
Previous suggestions based on analytical solutions to the water flow problem
A new approach• The new, proposed approach for the design of a drip
irrigation system is based on a different principle of evaluating the water use efficiency (RWUR ≡ water uptake rate relative to water supply rate) in a source (emitter) – sink (rooting zone) system, so the potential water uptake is not given (/prescribed) but computed.
• The potential (maximum possible) water uptake is evaluated assuming no local soil-plant resistance to uptake. Namely, the plant roots apply maximum possible suction and the water uptake is determined just by the soil’s ability to conduct water from the sources (emitters) to the sinks (rooting zones).
Coupled source-sink model
r0
d0
water source
point sink, qsi
actual sink
potential sink
reference suction point: ϕf = ϕso - qsiϕsi = 0
(uzθ) = -mαϕ(r,0)/2 evaporation:
r
z soil sorptive number: α
( )( )botsi
botsosi ,0
,0ΖΦΖΦ
=q
The RWUR is evaluated from:
α−1 – soil’s capillary lengthr0 – radius of the rooting zonem – potential evaporation
Model assumptionsThe relative water uptake rate will be evaluated with an analytical solution under the following assumptions:• Steady flow (resulting in maximum uptake rate)• A homogenous, isotropic and exponential (Gardner, 1958) soil: K = Ksat e-αh
• Linearization of the flow problem with Kirchoff transformation: • The solution for the water uptake and for the spatial distribution of water contents is a superposition of the fundamental solutions for water infiltration from point or line sources: positive sources representing the emitters and negative sinks representing the root systems• The maximum possible water uptake will be evaluated assuming maximum suction in a volume of rooting zone with a simple geometry (sphere, horizontal cylinder) and given depth and size, the point (/line) sink located in its center.• Evaporation from the soil surface will be assumed proportional to the matrix flux potential, ϕ: (uzθ) = -mαϕ(r,0)/2 (following Lomen and Warrick, 1978)
∫ ∞−=
hKdhϕ
Coupled source-sink model: loam, 2 l/h dripperstream lines, saturation degrees stream lines, hydraulic heads
qsi = 0.62
actual sink
dividing stream line
uptakedeep percolation
α = 0.04 cm-1
0 25 50
75
50
25
0Sf = 1
0.49
0.590.76Hf = -60
z, cm
r, cm0 25 50
-199
-156
-129
-179
-91
Soil 3
r, cmConceived root zone: r0 = 25 cm
Effect of soil typecoarse sand (α = 0.4 cm-1) loam (α = 0.04 cm-1)
75
50
25
0
0.04
0.060.10.17
z, cm
a
Sf = 0.33
So
0 25 50
75
50
25
0Sf = 1
0.49
0.590.76
z, cm
r, cm
So
qsi = 0.62qsi = 0.52
02 =∂∂
−∇zϕαϕ
0 25 50
75
50
25
0
0.37
0.49
Sf = 1
0.67
z, cm
r, cm
Soil
Effect of evaporation from soil surfacewith evaporation (m=2) without evaporation
qsi = 0.62qsi = 0.40;qE = 0.43
uptake deep percolation
evaporation
0 25 50
75
50
25
0Sf = 1
0.49
0.590.76
z, cm
r, cm
So
uzθ = -mαϕ(r,0)/2 qE = m/(m+2)
Determining the values of the 3 parameters: α,r0,m •α−1 – “capillary length” characterizes the soil texture ( K = Ksat e-αh)α- influence of gravitational vs capillary forcesCharacteristic values:
coarse sand: 0.4 cm-1
loamy sand: 0.13 cm-1
loam: 0.04 cm-1
clay: 0.004 cm-1
• r0 – characterizes the extent of the rooting zonecarrot, radish: 10cm, pepper: 15cm, tomato: 25cm; cotton, corn: 50cm
•m – characterizes the potential evaporation (uzθ) = -mαϕ(r,0)/2• a crop that cover the soil surface: m = 0• Overall relative evaporation from on-surface emitters: qE = m/(m+2)
0 1 2 3 4 50.00
0.03
0.06
0.09 cyclical tests
α (c
m-1)
Ks (cm h-1)
Besor experimental station
α(cm) = 0.04035 Ks(cm/h)1/2
Sample Scenarios for drip irrigation
yso = 2 ysi
ysi
xso
xsi = 2xso
f
0.5
0.6
0.7
0.8
0.9
1.0
Coupled line source/sink
YSI=0.5
Coupled point source/sink
1
5432
q si/q
so
a
Plants-emitters along a dripline: emitter near each plant
ysi – distance between emitters, Ysi = αysi/2
Sample computation:pepper: r0 = 15 cmsand: α = 0.1 cm-1
distance between emitters:ysi = 40 cmR0 = αr0/2 = 0.75Ysi = αysi/2 = 2Relative water uptake:⇒ qsi/qso = 0.69
ysi = yso
R0 = αr0/2; D0 = αd0/2 = 0
[ ] [ ]
[ ] [ ]∑
∑Ν
=
Ν
=
ΥΦ+Φ
ΖΥΦ+ΖΦ
=
−
si
si1
10sisi0si
1botsisobotso
si
R,,02R,0,0
,,02,0,0
j
j
j
j
q
ββ
1siso ==ΥΥ β
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5.
Ro
m = 0 (no evaporation)
r0 small (cm) r0 large (cm)clay sand
Additional emitter in between plants
yso
ysi = 2yso
[ ] [ ]
[ ] [ ]∑
∑Ν
=
Ν
=
ΥΦ+Φ
ΖΥΦ+ΖΦ
=
−
si
si1
10sisi0si
1botsisobotso
si
R,,02R,0,0
,,02,0,0
j
j
j
j
q
ββ
5.0siso ==ΥΥ β
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5
Ro
0.30.40.50.60.70.80.9
1
5432
Ysi = 0.5a
0.5(q
si/qso)
5.0siso ==ΥΥ β
0.00.10.20.30.40.50.60.70.80.91.0
41
(qsi/qso)cent+(qsi/qso)intr
32Ysi = 0.5
43 (qsi/qso)intr
(qsi/qso)cent
a
q si/qso
Additional plant in between emitter
close
distant
closeclose distant
overall
yso = 2 ysi
ysi
=+
=+•
•
2sisi
1sisi
dqaqb
dqbqao
o
( ) [ ]∑Ν
=ΥΦ+Φ=
si
10sisi0si R,2,02R,0,0
jja
( )[ ]∑Ν
=Υ+Φ=
si
00sisi R,12,02
jjb
( ) ( )∑−Ν
=ΖΥΦ+ΖΦ=
1si
1botsisobotso1 ,,02,0,0
ββ
jjd
( )( )∑−Ν
=ΖΥ+Φ=
1si
0botsiso2 ,12,02
β
jjd
2siso ==ΥΥ β
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.50.0
Ro
Watering a plant row with one or two drip lines at different distances(Bell pepper, sandy soil, Besor experimental station, Meiri et al., 2011)
Photographed soil cross sections (perpendicular to the plant row) showing the root distribution in one-sided (top right) and two-sided (top left) irrigation at 0 distance
and one-sided at disatnce of 60 cm (bottom)
Comparison of measured plant growth and predicted RWUR
Measured plant growthEvaluated Relative Water Uptake Rate
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0 10 20 30 40 50 60
Pot
entia
l rel
ativ
e w
ater
upt
ake
rate
Driplines distance from plant (cm)
two-side
one-side
a
60
70
80
90
100
110
120
130
140
150
160
0 10 20 30 40 50 60
Pla
nt d
ry w
eigh
t (g/
plan
t)
Driplines distance from plant (cm)
two-side
one-side
b
Sources and sinks offset from the center of a confined rectangular domain
An alternative for using superposition to represent beds with few plant rows and driplines
Y Y
Y Y
-Y -Y
-Y -Y
X X
X X
A A A A
A A A A
B
B
B
B
B B
B
B
B B
B
B
a) 1 source – 1 sink b) 1 source – 2 sinks
c) 2 sources – 1 sink d) 2 sources – 2 sinks
One or Two drip lines per plant rowBell pepper, Besor Experimental Station, 2010
2DL 1DL 2DL 1DL June September
RWUR as a function of root system size for the various scenarios
B = 0.25 ; A/B = 2 B = 0.25 ; A/B = 4
Y Y
Y Y
-Y -Y
-Y -Y
X X
X X
A A A A
A A A A
B
B
B
B
B B
B
B
B B
B
B
a) 1 source – 1 sink b) 1 source – 2 sinks
c) 2 sources – 1 sink d) 2 sources – 2 sinks
1DL
1DL
2DL
2DL
Markers:B = 0.25 ; A/B = ∞
Two extreme scenarios forsub-surface drip irrigation
Early season:rooting zoneabove emitter
Mature stage: rooting zonebellow emitter
r0
zso water source
point sink, qsi
actual sink
potential
reference suction point: ϕf = ϕso - qsiϕsi = 0
soil surface
a
0.35
0.40
0.45
0.50
0.55
0.60
0.65
0.70
0.75
0 0.1 0.2 0.3 0.4 0.5
q Si/q
so
zso
b) R0 = 2; Ysi = 2
0.00.51.01.52.0
0.70
0.75
0.80
0.85
0.90
0.95
0 0.1 0.2 0.3 0.4 0.5
q Si/q
so
zso
a) R0 = 0.1; Ysi = 0.1
RWUR as function of emitter burial depth (Zso)and potential evaporation (m)
no evaporation m:
Zsi = Zso + R0
no evaporation
strong evaporationstrong evaporation
Plants of small root systems (clayey soil)at small spacing along the drip line
Plants of large root systems (sandy soil)at large spacing along the drip line
Effect of changes in hydraulic conductivityon conduction in the soil profile and local resistance
Relative water uptake rates (qsi/qso) for a rectangular array (120 x 30 cm) and conceived radius ofr0 = 15 cm, in a loam of Ks
0 = 1 cm h-1 (α = 0.04035 cm-1).
ζ = (Ks0/Ks -1)
Φsi/Φso(α)
RWUR = Φsi/Φso∙(1/(1+ζ))
0 1 2 3 4 50.00
0.03
0.06
0.09 cyclical tests
α (c
m-1)
Ks (cm h-1)
water conduction in the soil profile
local resistancewater uptake
α(cm) = 0.04035 Ks(cm/h)1/2
Unsteady (transient) water flow and uptake
0 24 48 72
q so
0 24 48 72
ζ,W
UR
r0
water source, qso
point sink, qsi
actual sink
conceived rooting zone
reference suction point:
ϕf = Σϕso(t) – (qsi/qso)(ϕsi+ξ(t)) = 0 zbot
z∗
tst tst+ttr
W0
t0
soil coefficients: α, β
Daily Irrigation Scenarios
Single morning irrigationContinuous, all day irrigationMultiple pulse irrigations
Transient model predictions of daily water uptake patterns from one-hour and continuous (12h) irrigation in a fine sand
0 6 12 18 240
20
40
60
80
100β = 0
c
1h 12h
WUR
(cm3 h-1
)
Time (h)0 6 12 18 24
β = -0.75 1h 12h
d
Time (h)
α = 0.04 cm-1, Ks = 10 cm h-1, r0= 15 cm, rc= 30 cm, m = 0 (no evaporation)
homogeneous Ks decreasing with depth soilsKs(z) = Ks (0)e-βz
0 6 12 18 240.0
0.2
0.4
0.6
0.8
1.0 one pulse per day ten pulses per day
q si/qso
time (h)Assouline et al. 2006
steady flowRelative Water
Uptake Rate
weatherpotential evaporation
soilsorptive length
plantdiameter of root zone
(distance between plants)
distance between
emitters & driplines
aSoil
sat. hydraulic conductivity,
sorptive length, porosity
unsteady flowRelative WaterUptake Volume b
irrigation frequency
water consumption
durationof
irrigation
c
starting hour of irrigation
d
Irrigationdoze
Plant-Weatherdiurnal transpiration
resistance pattern
emitter discharge
rate
f
e
f
e
Quasi-steady flowRelative WaterUptake Volume
Weather: diurnal pattern of potential evaporation
g
g
A New Approach for the Design and Scheduling
DIDAS main window for choosing among the steady, quasi-steady and unsteady
modeling for the design and scheduling
http://app.agri.gov.il/didas
DIDAS window for choosing between theCoupled Source-Sink Systems
with On-surface or Sub-surface emitters
An example of DIDAS Scenarios for Drip Irrigation
The water flow and uptake problem can be formulated in two, equivalent modes:1.Superposition of neighboring
sources and sinks2.Flow in a laterally-confined,
equivalent domain
An example of DIDAS steady modeling output:RWUR as function of the radius of the root zone for various
distances of plants and emitters along the driplines
DIDAS window defining the irrigation scheduling scenario:Daily, 2h-irrigation at 6:00
Sample of DIDAS unsteady model output:Diurnal patterns of the RWUR
Conclusion (1) •The proposed coupled source/sink model allows evaluating:
the RWU rate when using steady-state solutions and the RWU volume when using time-dependent solutions
•When the plant roots create maximum possible suction and there is no local soil-plant resistance the water uptake is determined just by the capability of the soil to conduct water from the sources to the sinks.•We suggest that this RWUR is maximal for the given source/sink geometry and propose to use it as a criterion for the design of drip irrigation systems. •The computations of the RWUR requires only a minimum number of 3 parameters describing the soil texture, the size of the root zoneand the potential evaporation, in the few cases when it is important to account for also evaporation form the soil surface.
Conclusion (2) •The design of drip irrigation systems can be made by superposing the solutions for water infiltration from sources to sinks: positive sourcesrepresenting the emitters and negative sinks representing the root systems.•The water flow and uptake problem can be formulated in two, equivalent modes: 1.Superposition of neighboring sources and sinks; 2. Flow in a laterally-confined, equivalent domain.
•The irrigation scheduling optimizing tool is based on a RWUV (ratio between daily water uptake volume and daily irrigation volume) criterion. •The computations of the diurnal patterns of the water uptake rates and the daily RWUV for a given irrigation scenario require additional information on the diurnal pattern of the plant resistance to water uptake and on the hydraulic conductivity of the soil. •The simulated scenario of irrigation scheduling should include a sufficient number of irrigation cycles (larger for clayey as compared to sandy soils) for approaching a quasi-steady periodic pattern.
Conclusion (3) •DIDAS includes also a module of quasi-steady flow for evaluating the diurnal water uptake patterns that accounts for the diurnal patterns of the plant resistance and evaporation and serves for fine-tuning of the design and preliminary evaluation of scheduling scenarios. •DIDAS was programmed in DELPHI and it runs on any Windows operating system-PC, with no further software requirements. The construction of the drip irrigation scenario is performed via few GUI windows, which contain also a library of the required input parameters, and several best-fitting procedures. •The computed RWURs and RWUVs are displayed graphically and the tabulated output results can be exported to e.g. Windows Excel for further processing.•DIDAS depicts the steady flow patterns (potentials and streamlines) for various geometrical and plant resistance scenarios and also the temporal patterns of the water potential at specified locations.